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SageMath
sage: E = EllipticCurve("x1")
sage: E.isogeny_class()
Elliptic curves in class 303450.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 303450.x1 | 303450x2 | \([1, 1, 0, -8294450, -54402943500]\) | \(-6693187811305/131714173248\) | \(-1241898416035763325000000\) | \([]\) | \(55987200\) | \(3.3042\) | |
| 303450.x2 | 303450x1 | \([1, 1, 0, 917425, 1964519625]\) | \(9056932295/181997172\) | \(-1716003631622995312500\) | \([]\) | \(18662400\) | \(2.7549\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.x have rank \(0\).
Complex multiplication
The elliptic curves in class 303450.x do not have complex multiplication.Modular form 303450.2.a.x
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
